Biophysical Chemistry 105 (2003) 559–572 Thermodynamic and extrathermodynamic requirements of enzyme catalysis Richard Wolfenden* Department of Biochemistry and Biophysics, University of North Carolina, Chapel Hill, NC 27599-7260, USA Received 24 October 2002; received in revised form 22 January 2003; accepted 22 January 2003 Abstract An enzyme’s affinity for the altered substrate in the transition state (symbolized here as S‡) matches the value of kcatyK m divided by the rate constant for the uncatalyzed reaction in water. The validity of this relationship is not affected by the detailed mechanism by which any particular enzyme may act, or on whether changes in enzyme conformation occur on the path to the transition state. It subsumes potential effects of substrate desolvation, H- bonding and other polar attractions, and the juxtaposition of several substrates in a configuration appropriate for reaction. The startling rate enhancements that some enzymes produce have only recently been recognized. Direct measurements of the binding affinities of stable transition-state analog inhibitors confirm the remarkable power of binding discrimination of enzymes. Several parts of the enzyme and substrate, that contribute to S‡ binding, exhibit extremely large connectivity effects, with effective relative concentrations in excess of 108 M. Exact structures of enzyme complexes with transition-state analogs also indicate a general tendency of enzyme active sites to close around S‡ in such a way as to maximize binding contacts. The role of solvent water in these binding equilibria, for which Walter Kauzmann provided a primer, is only beginning to be appreciated. ᮊ 2003 Elsevier Science B.V. All rights reserved. Keywords: Transition state; Binding; Enzyme catalysis; Inhibition; Thermodynamics 1. Introduction uate at Princeton, I had the good fortune of listening to Professor Kauzmann’s lectures on As he laid the foundations for the present physical chemistry. Those lectures offered a brac- understanding of protein folding, Walter Kauz- ing antidote to the encyclopedic monotony with mann identified the pervasive influence of solvent which organic chemistry was taught in those days. water on cellular processes, and the importance of Walter did not gloss over the difficulties. In one considering solution thermodynamics before seek- of his more delphic utterances, he once exclaimed ing more exotic explanations of the rates and ‘‘Anyone who thinks that he understands entropy equilibria on which life depends. As an undergrad- is crazy!’’ The visionary biochemist Fritz Lipmann, with *Tel.: q1-919-966-1203; fax: q1-919-966-2852. whom I carried out my doctoral work, had already E-mail address: [email protected] (R. Wolfenden). begun to teach biochemists the importance of free 0301-4622/03/$ - see front matter ᮊ 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0301-4622Ž03.00066-8 560 R. Wolfenden / Biophysical Chemistry 105 (2003) 559–572 energy changes during metabolism. During that toward the structure that it adopts in the transition period, I also learned from William Jencks and state w2x. In his remarkable textbook, written only Frank Westheimer that the reactivities of organic a few years later w3x, Schwab explains: compounds could be described in the language of physical chemistry, bringing the genuinely organic The energy barrier to be overcome is lowered in the chemistry of living systems within the reach—if adsorption layer because the activated state is strongly not necessarily the grasp—of people with a quan- adsorbed and, therefore, in the adsorption layer, is less endothermic and therefore more often reached. Hence, it is titative bent. When I returned as an assistant not that the adsorbate is activated but that the adsorbate is professor to Walter’s department, I benefited from (more) easily activated and is therefore, at equilibrium, his hunch that the future vitality of academic present in the activated state to a greater percentage extent chemistry lies in its application to biological ques- than in the free gas. tions. The impact of his teaching, on me as on so many others, has been remarkable. If ‘active site’ is substituted for ‘adsorption layer’, this statement contains the essence of our 2. Thermodynamic requirements of an efficient present view of how free energy changes accom- catalyst pany enzyme catalysis in aqueous solution. 3. ‘Adsorption of the activated state’ by Enzyme–substrate interactions have long been enzymes recognized as representing an extreme expression of structural complementarity in biological chem- Many years after Polanyi’s paper, and with no istry. One of the earliest observations to emerge apparent knowledge of its existence, Linus Pauling from studies of catalysis by enzymes, and from w4x and William Jencks w5x speculated that it might heat inactivation of enzymes in the presence of be possible to develop a powerful enzyme antag- small molecules, was that enzymes bind substrates onist in the form of an unreactive compound, reversibly, forming complexes that appear to dis- analogous in structure to S‡ , the altered substrate sociate at concentrations usually slightly higher in the transition state. Then, in 1969, the algebra than those that are present physiologically. Unreac- in Scheme 1 was used to show that an ideal tive structural analogs of the substrate are usually ‘transition-state analog’ should surpass a conven- found to be reversible inhibitors. This suggests tional substrate or product in its affinity for the that substrates and substrate analogs vie for a place enzyme, by a factor that matches or surpasses the on the enzyme, in accord with the possibility that very large (see below) rate enhancement that the ES complexes are also formed during the catalytic enzyme produces w6x. transformation of the substrate (for a review, see Because of its startling implications for catalysis w1x). This view led to the well-known proposal by and inhibitor design, it seems worthwhile to con- Emil Fischer that substrates fit enzymes as a key sider some qualifications and questions raised by fits a lock. Captivated by that image, medicinal this scheme. chemists occupied themselves for many decades in designing substrate-like inhibitors, hoping that 1. Must an enzyme bind S‡ more tightly than S? they would be strong and enzyme-specific. If enzymes did not stabilize transition states, But was Fischer’s view correct? In considering no increase in rate would occur. The algebra that question, it is helpful to focus attention on the of Scheme 1 tells us that to lower the free various stages through which a substrate passes as energy of activation, an enzyme must bind S‡ it undergoes chemical activation. To enhance the more tightly than S. Accordingly, the distinc- rate of a reaction, a catalyst must enhance the tion that was once made between ‘binding substrate equilibrium constant for attaining the sites’ and ‘catalytic sites’ appears meaningless, transition state. As early as 1921, Polanyi recog- since catalysis depends on this transient nized that a catalyst must bind a reactant with increase in binding affinity. When two sub- increasing affinity as the reactant is distorted strates are compared, specificity may appear in R. Wolfenden / Biophysical Chemistry 105 (2003) 559–572 561 sheep near a mountain pass. If we could illuminate the sheep with an instantaneous flash of light, we would observe that their population dwindled with increasing height. These sheep are not wandering with any pur- pose and have no inherent tendency to congre- gate near the most direct path to the transition state. The enzyme is designed in such a way that the rarer the species of the substrate (between S and S‡), the more tightly it is bound, near the path to the transition state w7x. 3. Must the native enzyme be a pre-existing ‘template’ for the altered substrate in the tran- sition state? No. Scheme 1 rests on no assump- tions about the presence or absence of changes in the conformation of an enzyme during catalysis. Scheme 1 implies that an enzyme is a template that is in, or can easily adopt (i.e. without much distortion of the enzyme from its native structure, as expressed in free energy) a conformation complementary to that of the substrate in the transition state. The forces of attraction in the transition state are so strong Scheme 1. If equilibrium is maintained between the ground state and the transition state in dilute solution, then the formal that it would be surprising if some change in dissociation constant of the altered substrate in the transition enzyme structure did not occur. Moreover, ( ) state Ktx is expected to be less than that of the substrate in changes in enzyme conformation, as discussed ( ) the ground state Km , by a factor matching the factor by which below, are probably needed to reconcile maxi- ( ) the rate constant of the catalyzed reaction kcat exceeds that ( ) mal forces of attraction in the transition state of the uncatalyzed reaction knon . Effects of desolvation, ( charge separation or proximity in multisubstrate reactions can tending to involve a closed structure of the be considered to involve subpopulations of ES that depart from active site), with the conflicting need for rapid the mean in the usual statistical description of molecules in the substrate access to, and product egress from, ground state. At equilibrium, any of these subpopulations can an open structure w8x. Structural evidence for be more reactive than ES, but can do so only to the extent that such changes, obtained from the crystal struc- it is rare. Transition-state affinity may be underestimated if the mechanism of reaction in solution differs fundamentally from tures of enzyme complexes with transition- the mechanism of reaction at the enzyme’s active site, or state analogs, is now so abundant that it kKcat m is limited by enzyme–substrate encounter. This relation- appears to be the rule rather than the exception. ship is not applicable to reactions involving quantum mechan- 4.